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This paper investigates multiple attribute decision making (MADM) problems in which the attribute values take the form of interval-valued dual hesitant fuzzy elements (IVDHFEs). Firstly, motivated by the concepts of dual hesitant fuzzy set (DHFS) and interval number, the concept, operational laws and comparison laws of interval-valued dual hesitant fuzzy elements are proposed. Then, based on the operational laws of IVDHFEs, some aggregation operators are developed for aggregating the interval-valued dual hesitant fuzzy information, such as the interval-valued dual hesitant fuzzy weighted aggregation operators, the interval-valued dual hesitant fuzzy ordered weighted aggregation operators, the generalized interval-valued dual hesitant fuzzy weighted aggregation operators, the generalized interval-valued dual hesitant fuzzy ordered weighted aggregation operators and the interval-valued dual hesitant fuzzy hybrid aggregation operators. Furthermore, some desirable properties of these operators and the relationships between them are discussed in detail. Based on the interval-valued dual hesitant fuzzy weighted average (IVDHFWA) operator, an approach to multiple attribute decision making is proposed under interval-valued dual hesitant fuzzy environment. Finally, a numerical example is given to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]